Note that the back-door path \(X \!\leftarrow \!S \rightarrow Y\)  contributes a spurious correlation between \(X\)  and \(Y\)  [1]}, where \(S\)  acts as a confounder. The existence of back-door path is the key challenge for achieving unbiasedness across balanced and imbalanced test data. Simply learning by \(P(Y|X=x)\)  will inevitably include such spurious correlation, which is not what we seek to estimate, and lead to a biased model. Therefore, we instead estimate \(P(Y|do(X=x))\)  which can eliminate the confounding bias to obtain an unbiased model.
